Lie Algebras and Algebraic Groups (Springer Monographs in Mathematics)

Book Description

The theory of Lie algebras and algebraic groups has been an area of active research for the last 50 years. It intervenes in many different areas of mathematics: for example invariant theory, Poisson geometry, harmonic analysis, mathematical physics. The aim of this book is to assemble in a single volume the algebraic aspects of the theory, so as to present the foundations of the theory in characteristic zero. Detailed proofs are included and some recent results are discussed in the final chapters. All the prerequisites on commutative algebra and algebraic geometry are included.

Galois Representations in Arithmetic Algebraic Geometry (London Mathematical Society Lecture Note Series)

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Galois Representations in Arithmetic Algebraic Geometry (London Mathematical Society Lecture Note Series)

Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Paperback

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ASIN: 0521644194

Book Description

This book is a conference proceedings based on the 1996 Durham Symposium on "Galois representations in arithmetic algebraic geometry". The title was interpreted loosely and the symposium covered recent developments on the interface between algebraic number theory and arithmetic algebraic geometry. The book reflects this and contains a mixture of articles. Some are expositions of subjects that have received substantial recent attention: Erez on geometric trends in Galois module theory; Mazur on rational points on curves and varieties; Moonen on Shimura varieties in mixed characteristics; Rubin and Scholl on the work of Kato on the Birch-Swinnerton-Dyer conjecture; and Schneider on rigid geometry. Some are research papers by: Coleman and Mazur, Goncharov, Gross, Serre.

Combinatorial Commutative Algebra (Graduate Texts in Mathematics)

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Coherent and Useful

Combinatorial Commutative Algebra (Graduate Texts in Mathematics)
Ezra Miller , and Bernd Sturmfels
Manufacturer: Springer
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Binding: Paperback

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ASIN: 0387237070

Book Description

Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters cover a broad spectrum of topics, ranging from homological invariants of monomial ideals and their polyhedral resolutions, to hands-on tools for studying algebraic varieties with group actions, such as toric varieties, flag varieties, quiver loci, and Hilbert schemes. Over 100 figures, 250 exercises, and pointers to the literature make this book appealing to both graduate students and researchers.

Customer Reviews:

Coherent and Useful.......2006-07-25

This book does a good job at introducing some of the most interesting combinatorial problems in monomial resolutions. Although their chapter on toric varieties is somewhat weak, most of the other chapters (square-free monomial ideals, Borel-fixed ideals, staircases associated to monomial ideals in three variables, etc.) are very well written with challenging and revealing exercises at the end.

Generic Polynomials: Constructive Aspects of the Inverse Galois Problem (Mathematical Sciences Research Institute Publications)

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Generic Polynomials: Constructive Aspects of the Inverse Galois Problem (Mathematical Sciences Research Institute Publications)
Christian U. Jensen , Arne Ledet , and Noriko Yui
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521819989

Book Description

This book describes a constructive approach to the Inverse Galois problem. The main theme is an exposition of a family of "generic" polynomials for certain finite groups, which give all Galois extensions having the required group as their Galois group. The existence of such generic polynomials is discussed, and where they do exist, a detailed treatment of their construction is given. The book also introduces the notion of "generic dimension" to address the problem of the smallest number of parameters required by a generic polynomial.

Local Algebra (Springer Monographs in Mathematics)

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Serre as usual

Local Algebra (Springer Monographs in Mathematics)
Jean-Pierre Serre
Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540666419

Book Description

This is an English translation of the now classic "Algèbre Locale - Multiplicités" originally published by Springer as LNM 11, in several editions since 1965. It gives a short account of the main theorems of commutative algebra, with emphasis on modules, homological methods and intersection multiplicities ("Tor-formula"). Many modifications to the original French text have been made by the author for this English edition: they make the text easier to read, without changing its intended informal character.

Customer Reviews:

Serre as usual.......2005-11-02

This book is crystal clear and reads like a bedtime story. I wish I had it when I took commutative algebra.

Representations of Quantum Algebras and Combinatorics of Young Tableaux

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Representations of Quantum Algebras and Combinatorics of Young Tableaux
Susumu Ariki
Manufacturer: American Mathematical Society
ProductGroup: Book
Binding: Mass Market Paperback

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Book Description

This book contains most of the nonstandard material necessary to get acquainted with this new rapidly developing area. It can be used as a good entry point into the study of representations of quantum groups.

Among several tools used in studying representations of quantum groups (or quantum algebras) are the notions of Kashiwara's crystal bases and Lusztig's canonical bases. Mixing both approaches allows us to use a combinatorial approach to representations of quantum groups and to apply the theory to representations of Hecke algebras.

The primary goal of this book is to introduce the representation theory of quantum groups using quantum groups of type $A_{r-1}^{(1)}$ as a main example. The corresponding combinatorics, developed by Misra and Miwa, turns out to be the combinatorics of Young tableaux.

The second goal of this book is to explain the proof of the (generalized) Leclerc-Lascoux-Thibon conjecture. This conjecture, which is now a theorem, is an important breakthrough in the modular representation theory of the Hecke algebras of classical type.

Product Description

The book contains several well-written, accessible survey papers in many interrelated areas of current research. These areas cover various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie superalgebras. Geometric methods have been instrumental in representation theory, and these proceedings include surveys on geometric as well as combinatorial constructions of the crystal basis for representations of quantum groups. Humphreys' paper outlines intricate connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic, left cells in two sided cells of affine Weyl groups, and the geometry of the nilpotent orbits. All these papers provide the reader with a broad picture of the interaction of many different research areas and should be helpful to those who want to have a glimpse of current research involving representation theory.

Groups as Galois Groups: An Introduction (Cambridge Studies in Advanced Mathematics)

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Groups as Galois Groups: An Introduction (Cambridge Studies in Advanced Mathematics)
Helmut Volklein
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover

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ASIN: 0521562805

Book Description

This book describes various approaches to the Inverse Galois Problem, a classical unsolved problem of mathematics posed by Hilbert at the beginning of the century. It brings together ideas from group theory, algebraic geometry and number theory, topology, and analysis. Assuming only elementary algebra and complex analysis, the author develops the necessary background from topology, Riemann surface theory and number theory. The first part of the book is quite elementary, and leads up to the basic rigidity criteria for the realization of groups as Galois groups. The second part presents more advanced topics, such as braid group action and moduli spaces for covers of the Riemann sphere, GAR- and GAL- realizations, and patching over complete valued fields. Graduate students and mathematicians from other areas (especially group theory) will find this an excellent introduction to a fascinating field.

Algebra IX: Finite Groups of Lie Type. Finite-Dimensional Division Algebras (Encyclopaedia of Mathematical Sciences)

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Algebra IX: Finite Groups of Lie Type. Finite-Dimensional Division Algebras (Encyclopaedia of Mathematical Sciences)

Manufacturer: Springer
ProductGroup: Book
Binding: Hardcover

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ASIN: 3540570381

Book Description

The first contribution covers the theory of finite groups of Lie type, which is an important field of current mathematical research. After giving the basic information Carter describes the Deligne-Lusztig method of obtaining characters of these groups using l-adic cohomology and subsequent work of Lusztig.The second part by Platonov and Yanchevskii surveys the structure of finite-dimensional division algebras and includes an account of reduced K-theory.

Book Description

Eye-opening essays by esteemed writers about the rich and complicated lives of American stepfamilies.

With the U.S. divorce rate hovering around 50 percent, most people recognize remarriage as a now-familiar occurrence. And remarriage often means stepfathers, -mothers, -brothers, and -sisters, and the formation of a new type of blended family. Jacquelyn Mitchard, Barbara Kingsolver, Roxana Robinson, Susan Cheever, and others share experiences of being stepdaughters, stepmothers, or ex-wives. Andrew Solomon writes about his relationship with his stepmother. Kate Christensen celebrates the stepfather who brought guidance to her life. There are essays from writers in the same family, each with a different take on his or her postnuclear situation: Phyllis Rose discusses her second husband's qualities as a stepfather, while her son, Ted Rose, writes about his tumultuous relationship with his stepbrother from his own father's remarriage. These poignant, heartfelt, sometimes biting tales remind us of the outdated myth of the perfect nuclear family while shedding light on what it means to forge relationships with stepfamily members.

Customer Reviews:

Great family relations insights on every page.......2007-05-22

The subject matter here is ideal for writers. By definition, every relationship having a step-someone in it came about following death or divorce in the family -- so the universal themes of personal loss and renewal provide the overarching themes of each one of these pithy 7-to-10-page essays, which immerse us in the most profound of human struggles. I could have read dozens more of these stories of sundered and resurrected family ties, and fervently hope the editor will bring out a supplemental volume every year.

A Portrait of the Families We Inhabit.......2006-11-08

This inspiring book of essays is a natural choice for anyone who is a stepparent or stepchild and therefore part of the modern phenomenom of a blended family. In many ways the book casts an even wider appeal because so many of the essays are about the struggles we all face in modern family life--how to live with people in your family who may have different desires and outlooks in life than your own. I really loved this book, and I found myself alternately laughing out loud (Phyllis Rose's piece on her absent-minded second husband was endearing and hilarious), wincing (Dana Kinstler's essay on father-love was all too familiar), and crying (Stephanie Stokes Oliver's piece on her love for her stepdaughters moved me). I ended up buying more copies of this book and handing them out to my sister, my friend from business school who is a stepmother, my stylist (no kidding) who lost her father when she was two. The essays are short enough to read one a night before falling asleep--my favorite time of the day to read. This is definitely a great gift idea for yourself or someone else in your life.

Touching, Engaging Stories about Family Relationships.......2006-05-19

The personal stories in this collection are moving and the writing so incredibly revealing. You get so many different points of views, shared experiences from stepmothers, stepfathers, from stepchildren. You get it all and each story is beautifully written - some are funny, witty; some are sad; some are triumphant. It's a wonderful read even for those who don't have the shared stepfamily experiences like myself. I loved it!

Brilliantly Insightful Stories about Families.......2006-05-16

I began reading this book for its gossip value -- I was curious to understand the intimate lives of some of the famous writers whose essays are included here. I assumed that I wouldn't actually relate personally to the stories because I'm not part of a step-family. But in fact these stories gave me tremendous insights into my relationship with my father and my mother, old boyfriends, and also into the kind of person I am -- simply because the essays are full of tremendously acute observations about relationships as well as fascinating and delicious scenes.
Every time I finished an essay I couldn't help myself from plunging immediately into the next, reading the chapters in exactly the order assembled (after checking out the work of the writers about which I was most curious). This is SUCH a good book! I kept putting stars in the margins and thinking, Oh I want to copy that into my notebook -- because what's illuminated is the "ordinary" family, too. The first essay (by Dana Kinstler) made me think about the roles of daughters and fathers, and then in Phyllis Rose's I was thinking about whether my own father had provided enough strength and direction for me to feel secure (apparently not) and Sasha Troyan's lovely and droll and funny piece made me think about how people look while they are falling in love, and Andrew Solomon's made me marvel about the sort of people able to get a tremendous amount done, and the nature of parental love, and a thousand other things. I ADORED the quirky, funny, touching essays by D. S. Sulaitis (who I'd never heard of; now I'm dying to read more by her) and Sandra Tsing Loh, and the haunging one by Alice Elliott Dark, and the heartbreaking one by Jacquelyn Mitchard -- but all of them taught me something. I found this to be such a useful, smart, absorbing book. It provides stories that give insight into one's own life (which is what I for one really want stories to do). Actually, this book did feel like good gossip - but the kind that illuminates your own life.

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